Context. Empirical stellar spectral libraries have applications in both extragalactic and stellar studies, and they confer an advantage over theoretical libraries because they naturally include all relevant chemical species and physical processes. In recent years we have seen a stream of new sets of high-quality spectra, but increasing the spectral resolution and widening the wavelength coverage means resorting to multi-order echelle spectrographs. Assembling the spectra from many pieces results in lower fidelity of their shapes. Aims. We aim to offer the community a library of high-signal-to-noise spectra with reliable continuum shapes. Furthermore, the use of an integral field unit (IFU) alleviates the issue of slit losses. Methods. Our library was built with the MUSE (Multi-Unit Spectroscopic Explorer) IFU instrument. We obtained spectra over nearly the entire visual band (λ ∼ 4800–9300 Å). Results. We assembled a library of 35 high-quality MUSE spectra for a subset of the stars from the X-shooter Spectral Library. We verified the continuum shape of these spectra with synthetic broadband colors derived from the spectra. We also report some spectral indices from the Lick system, derived from the new observations. Conclusions. We offer a high-fidelity set of stellar spectra covering the Hertzsprung-Russell diagram. These can be used for both extragalactic and stellar studies and demonstrate that the IFUs are excellent tools for building reliable spectral libraries.